Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#23368 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle, prime radical | C23×C11 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21)(22,29)(23,27)(24,33)(25,28)(26,32)(30,35)(31,34)(36,37,40,43,39,42,47,50)(38,44,46,51,45,41,48,49);(14,19)(16,18)(20,22,25,32)(21,26,28,29)(23,31,24,30)(27,35,33,34);(12,14,15,19)(13,16,17,18)(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,34,29,35)(36,38,39,45)(37,41,42,44)(40,46,47,48)(43,49,50,51);(13,17)(16,18)(20,24,25,23)(21,27,28,33)(22,31,32,30)(26,34,29,35)(38,45)(41,44)(46,48)(49,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16356);